Trisection of an Angle : A Revised Approach

Author(s)	Omvir Singh Chaudhary
Country	India
Abstract	Angle trisection—dividing an arbitrary given angle into three equal smaller angles using only an unmarked straightedge and a compass—is one of the classical Greek problems of plane geometry. While traditional field theory proves the impossibility of exact classical trisection for arbitrary angles using strictly finite Euclidean operations, this paper proposes a revised geometric construction methodology based on systematic arc intersections and congruent arc property mapping. The presented method details an explicit step-by-step procedure capable of trisecting angles up to 180^\circ, accompanied by visual representations (Figures 1, 2, and 3), proof of arc congruence, and defined operational boundary conditions.
Keywords	Angle Trisection, Classical Construction, Euclidean Geometry, Congruent Arcs, Compass and Straightedge, Arc Trisection
Field	Mathematics
Published In	Volume 7, Issue 10, October 2026
Published On	2026-10-01

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